Question about equality in college sports

(I assume this belongs here rather than in IMHO - feel free to move it if necessary)

In California high schools, there is a rule that says that girls cannot play on a “boys’ team” if the school has a girls’ team at the same level (e.g. varsity) in the same sport. I am under the impression that this was forced upon the state by Title IX.

Is there something similar in college sports - for example, women can’t play “men’s” basketball? I have heard of women playing baseball and football, but as women’s baseball and women’s football are not NCAA sports (softball is not considered the same thing as baseball), such a rule wouldn’t apply. However, I have never head of a woman on a men’s college basketball team, and while it’s possible that the only women who have even considered it just weren’t good enough, it just seems a little hard to believe that it has never happened, considering the sheer number of teams.

Wouldn’t the fear be that men will demand a position on the women’s teams in the same sport?

It’s possible, but I haven’t heard of anybody putting that to the test.

Something else I have not heard happen at the college level, but have heard at the high school level; men trying to get on women’s field hockey teams because their schools do not support “men’s field hockey.” At high school level, some states do allow this, but some, if not all, have restrictions (e.g. an all-girls team has the right not to play a team with one or more boys on it - the danger is, there’s a good chance the boys’ slapshots are dangerously fast - without the game being counted as a forfeit); California’s rule is, a school can keep boys off of a team where the sport is pretty much girls-only (softball, field hockey, and, at most northern California schools, volleyball) if “the number of opportunities for boys and girls is equal” (which usually translates as, “if the school has a football team”).